A colleague showed me a problem from a publisher-created test on the Algebra II topic of sequences and series. The problem was horrid.
It's one thing to ask for the next three terms of an arithmetic sequence or of a geometric sequence. But to give a random sequence, and then expect there to be only one approved solution, frosts me. Why? Because it instills in the students a belief that math is whatever the teacher says it is, and that the object is to read the teacher's (or the publisher's) mind in order to get the correct answer. In math, the exact opposite of that belief is reality--but that's not what problems like the following imply.
Here's the problem: Give the next three terms of the sequence 5, 7, 10, 15, 23, ...
The approved solution from the publisher is
5, 7, 10, 15, 23, 35, 52, 75
How did they get this? Like this:
The problem is, since we haven't identified what kind of sequence we're talking about, there's another easy-to-come-by solution that is just as mathematically justifiable:
Both are correct because, again, we haven't identified what type of sequence this is. The solution key gives only the first answer, even though there are reasonable answers aplenty.
Bad, bad, bad.